Title:

Simulation of transient blood flow in models of arterial stenosis and aneurysm

The Large Eddy Simulation (LES) technique with the SmagorinskyLilly dynamic subgrid model and twoequation Standard kω Transitional turbulence model are applied to investigate nonspiral and spiral blood flow through three dimensional models of arterial stenosis and aneurysm. A spiral pattern of blood flow is thought to have many beneficial effects on hemodynamics. Previous computational studies on spiral blood flow involve only steady spiral flow in a straight stenosed pipe without considering an upstream curved section of the artery. But a spiral pattern in the blood flow may exist due to the presence of an upstream curved section in the artery. On the other hand, pressure is generally considered a constant quantity in studies on pulsatile flow through either arterial stenosis or aneurysm; however, blood pressure is a waveform in a physiological flow. Although cosinetype or smooth regular stenoses are generally taken in investigations of blood flow in a threedimensional model of arterial stenosis, in reality, stenoses are of irregular shape. Besides stenosis and aneurysm, another abnormal condition of the artery is the presence of stenosis with an adjacent aneurysm in the same arterial segment, especially in the posterior circulation. A study on (steady or pulsatile) flow through such arterial stenosis with an adjacent aneurysm in the same arterial segment is not available so far. Therefore, taking above things into consideration, thorough investigations of steady and unsteady pulsatile nonspiral and spiral blood flow in threedimensional models of stenosis and aneurysm are needed to give a sound understanding of the transitiontoturbulence of blood flow due to stenosis and aneurysm and to study the the effects of spiral velocity on the transitiontoturbulence. The LES technique has mostly been used to investigate turbulent flow in engineering fields other than biofluid mechanics. In the last decade, LES has seen its excellent potential for studying the transitiontoturbulence of physiological flow in biofluid mechanics. Though the kω Transitional model is used in few instances, mainly LES is applied in this study. Firstly, investigations of steady nonspiral and spiral blood flow through threedimensionalmodels of cosinetype regular stenosed tube without and with upstream curved segment of varying angles of curvature are performed by using the kω Transitional model and LES. A fully developed Poiseuille velocity profile for blood is introduced at the inlets of the models. To introduce a spiral effect at the inlet, onesixth of the bulk velocity is taken as the tangential velocity at the inlet along with the axial velocity profile there. Secondly, physiological pulsatile nonspiral and spiral blood flow through a threedimensional model of a straight tube having cosinetype regular stenosis are investigated by using mainly LES. A twoequation kω Transitional model is also used in one nonspiral flow case. The first four harmonics of the Fourier series of pressure pulse are used to generate physiological velocity profiles at the inlet. At the outlet, a pressure waveform is introduced. The effects of percentage of area reduction in the stenosis, length of the stenosis, amplitude of pulsation and Womersley number are also examined. Thirdly, transient pulsatile nonspiral and spiral blood flow through a threedimensional model of irregular stenosis are investigated by applying LES and comparison is drawn between nonspiral flow through a regular stenosis and that through an irregular stenosis. Lastly, pulsatile nonspiral and spiral blood flow through a threedimensional model of irregular stenosis with an adjacent poststenotic irregular aneurysm in the same arterial segment are studied by applying LES and the kω Transitional model. The effects of variation in spiral velocity are also examined. The results presented in this thesis are analysed with relevant pathophysioloical consequences. In steady flow through the straight stenosed tube, excellent agreement between LES results for Re = 1000 and 2000 and the corresponding experimental results are found when the appropriate inlet perturbations are introduced. In the models with an upstream curved segment, no significant effect of spiral flow on any flow property is found for the investigated Reynolds numbers; spiral pattern disappears before the stenosis – which may be due the rigid wall used in the models and/or a steady flow at the inlet. The effects of the curved upstream model can be seen mainly in the maximum turbulent kinetic energy (TKE), the maximum pressure drop and the maximum wall shear stress (WSS), which in the curved upstream models generally increase significantly compared with the corresponding results in the straight stenosed tube. The maximumcontributions of the SGS motion to the largescale motion in both nonspiral and spiral flow through a regular stenosis, an irregular stenosis and an irregular stenosis with an adjacent poststenotic irregular aneurysm are 50%, 55%and 25%, respectively, for the highest Reynolds number investigated in each model. Although the wall pressure and shear stress obtained from the kω Transitional model agree quite well with the corresponding LES results, the turbulent results obtained from the kω Transitional model differ significantly from the corresponding LES results – this shows unsuitability of the kω model for pulsatile flow simulation. Large permanent recirculation regions are observed right after the stenosis throat in both nonspiral and spiral flow, which in the model of a stenosis with an adjacent poststenotic aneurysm are stretched beyond the aneurysm and the length of the recirculation regions increases with spiral velocity. This study shows that, in both steady and unsteady pulsatile flow through the straight tube model having either a stenosis (regular or irregular) or an irregular stenosis with an adjacent poststenotic irregular aneurysm, the TKE rises significantly at some locations and phases if a spiral effect is introduced at the inlet of the model. However, the maximum value of the TKE in a high spiral flow drops considerably compared with that in a low spiral flow. The maximum wall pressure drop and shear stress occur around the stenosis throat during all the phases of the pulsatile cycle. In the model of a stenosis only, the wall pressure rises in the immediate poststenotic region after its drop at the stenosis throat. However, in the model of a stenosis with an adjacent aneurysm, the wall pressure does not rise to regain its undisturbed value before the start of the last quarter of the aneurysm. The effects of the spiral flow on the wall pressure and WSS are visible only in the downstream region where they take oscillatory pattern. The break frequencies of energy spectra for velocity and pressure fluctuations from −5/3 power slope to −10/3 power slope and −7/3 power slope, respectively, are observed in the downstream transitiontoturbulence region in both the nonspiral and spiral flow. At some locations in the transition region, the velocity spectra in the spiral flow has larger inertial subrange region than that in nonspiral flow. The effects of the spiral flow on the pressure spectra is insignificant. Also, the maximum wall pressure drop, the maximum WSS and the maximum TKE in the nonspiral flow through the irregular stenosis rise significantly compared with the corresponding results in the nonspiral flow through the regular stenosis. When the area reduction in the stenosis is increased, the maximum pressure drop, the maximumWSS and the TKE rise sharply. As for the effects of the length of the stenosis, the maximum WSS falls significantly and the maximum TKE rises sharply due to the increase in the length of the stenosis; but the maximum pressure drop is almost unaffected by the increase in the stenosis length.
